The present invention relates to pattern recognition and localization systems in general and, more particularly, to a priori and adaptive filtering for the detection of signals corrupted by noise. The pattern recognition and localization systems can be realized within a joint transform correlator architecture or within a frequency plane correlator architecture.
Broadly speaking, pattern recognition and localization systems are utilized for providing information regarding an input scene image with respect to a reference image. Pattern recognition and localization systems can be implemented by an all optical configuration, by a hybrid opto-electronic configuration as well as by electronic fully-digital processing apparatus as known in the art. For a discussion on the different configurations of pattern recognition and localization systems, reference is made to "Optical Signal Processing" by A. VanderLugt, John Wiley & Sons Ltd., 1992 which is incorporated herein by reference as if fully set forth herein. These systems are valuable tools used in a wide range of applications, including: machine vision, robotics, automation, surveillance systems, control of manufacturing processes, photogrammetry, and the like.
In principle, pattern recognition and localization architectures can be classified as either frequency plane correlators (FPCs) or as joint transform correlators (JTCs). The classification depends on the sequence and form in which the reference image, against which the input scene image is to be compared, is introduced into the filtering scheme.
The first known correlation architecture is the Frequency Plane Correlator (FPC). Up to the present time, there have been a number of designs of frequency plane masks for frequency plane correlators to accomplish pattern recognition and localization in a wide range of applications. These include the Classical Matched filter, Inverse filter, and Phase only filter as described in the above-mentioned reference: "Optical Signal Processing". Other filters include Nonlinear filters as described in an article entitled "Nonlinear Matched Filtering", by O. K. Ersoy and M. Zeng, J. Opt. Soc. Am. A. 6, 636-648 (1989).
It is well known that the Classical Matched filter is the optimum linear filter for extracting a known two-dimensional signal from additive, signal independent, stationary random noise by maximizing the detection Signal-to-Noise Ratio (SNR). The Classical Matched filter function for FPCs is R.sup.* (u,v)/P.sub.n (u,v) where R(u,v) is the Fourier transform of the reference image, P.sub.n (u,v) is a known a priori noise power spectral density and the asterisk .sup.* signifies a complex-conjugate operation. Overall, the cross correlation term of FPCs in the Classical Matched filter configuration is R.sup.* (u,v)S(u,v)/P.sub.n (u,v) where S(u,v) is the Fourier transform of the input scene image. However, the Classical Matched filter, as well as other designs mentioned hereinabove, suffer from a number of disadvantages which include that they do not provide a balanced trade-off between noise tolerance and peak sharpness which may be desirable for certain applications.
An alternative frequency plane mask design is the Wiener filter or more generally the parametric Wiener filter. Originally, Wiener filters were developed for image restoration in situations where an image was blurred and then corrupted by additive noise. The restoration of images was treated as the problem of finding an estimate that is a linear function of the data and minimizes the mean squared error between the true solution and itself, as described, for example, in an article entitled "Image restoration by the method of least squares" by C. W. Helstrom, J. Opt. Soc. Am. 57, 297-303 (1967).
It is well known that parametric Wiener filters, when used as frequency plane masks for FPCs, are particularly applicable for situations where a balanced trade-off between noise tolerance and peak sharpness, as reflected by the metrics Signal-to-Noise-Ratio and Peak-to-Correlation Energy Ratio, respectively, is required, as described in the article entitled "Filter design for optical pattern recognition: multi-criteria optimization approach" by Ph. Refregier, Optics Letters 15, 854-856 (1990). The Wiener filter function for FPCs is R.sup.* (u,v)/.vertline.R(u,v).vertline..sup.2 +P.sub.n (u,v)! whereas the parametric Wiener filter function for FPCs is R.sup.* (u,v)/.vertline.R(u,v).vertline..sup.2 +.gamma.P.sub.n (u,V)! where .gamma. is the filtering parameter. Overall, the cross correlation term of FPCs employing a Wiener filter is R.sup.* (u,v)S(u,v)/.vertline.R(u,v).vertline..sup.2 +P.sub.n (u,v)! whereas the cross correlation term of FPCs when employing a parametric Wiener filter is R.sup.* (u,v)S(u,v)/.vertline.R(u,v).vertline..sup.2 +.gamma.P.sub.n (u,v)!. It should be noted that both of these filter designs, as well as the Classical Matched filter, suffer from the disadvantage of their inability to compensate in the filtering process for input-additive random noise with an unknown a priori power spectral density in an adaptive manner.
The second correlation architecture is the so called Joint Transform Correlator (JTC) as described in an article entitled "A technique for optically convolving two functions", by C. S. Weaver & J. W. Goodman, Appl. Opt. 5, 1248-1249 (1966). Up to the present time there have been a number of designs of joint transform correlator configurations to deal with a wide range of applications. These include the nonlinear JTC described in U.S. Pat. No. 5,119,443 to Javidi and in the article entitled "Non-linear joint power spectrum based optical correlation" by B. Javidi, Appl. Opt. 28, 2358-2367 (1989), the fractional power joint transform correlator as described in an article entitled "Matched, phase only, or inverse filtering with joint-transform correlators" by H. Inbar & E. Marom, Optics Letters 18, 1657-1659 (1993) and the like. However, these designs suffer from a number of disadvantages which include that they are unable to compensate for colored noise inherent in an input scene image. This is true for cases where the noise power spectral density is either known or unknown a priori.
There is therefore a need for a number of novel filtering schemes for JTCs which are particularly suitable for compensating for stationary input-additive noise characterized by a wide range of a priori known power spectral densities ranging from white noise to colored noise models. Furthermore, there is a need for novel filtering schemes, for both FPCs and JTCs, which are adaptive to the random noise present in input scene images in cases where the noise power spectral density is unknown a priori.